Estimating Gaussian Curvatures from 3D Meshes

A new approach to estimate the surface curvatures from 3D triangular mesh surfaces with Gaussian curvature's geometry interpretation is proposed in this work. Unlike previous work, the proposed method does not use local surface fitting, partial derivative computation, or oriented normal vector recovery. Instead, the Gaussian curvature is estimated at a vertex as the area of its small neighborhood under the Gaussian map divided by the area of that neighborhood. The proposed approach can handle vertices with the zero Gaussian curvature uniformly without localizing them as a separate process. The performance is further improved with the local Bezier curve approximation and subdivision. The effectiveness of the proposed approach for meshes with a large range of coarseness is demonstrated by experiments. The application of the proposed method to 3D surface segmentation and 3D mesh feature extraction is also discussed.